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JAMB Mathematics Past Questions & Answers - Page 315

1,571.

The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms

Correct answer is B

T₂ = 4, T₄ = 16

T_x = ar^n-1

T₂ = ar^2-1 = 4 i.e. ar³ = 16, i.e. ar = 4

T₄ = ar^4-1

therefore, $\frac{T_4}{T_r}$ = $\frac{ar^3}{ar}$ = $\frac{16}{4}$

r² = 4 and r = 2

but ar = 4

a = $\frac{4}{r}$ = $\frac{4}{2}$

a = 2

Sⁿ = $\frac{a(r^n - 1)}{r - 1}$

S⁵ = $\frac{2(2^5 - 1)}{2 - 1}$

= $\frac{2(32 - 1)}{2 - 1}$

= 2(31)

= 62

1,572.

Find the sum of the first 18 terms of the series 3, 6, 9,..., 36.

505

513

433

635

View answer & explanation

Correct answer is B

3, 6, 9,..., 36.

a = 3, d = 3, i = 36, n = 18

S_n = $\frac{n}{2}$ [2a + (n - 1)d

S₁₈ = $\frac{18}{2}$ [2 x 3 + (18 - 1)3]

= 9[6 + (17 x 3)]

= 9 [6 + 51] = 9(57)

= 513

1,573.

Solve the inequality x2 + 2x > 15.

x < -3 or x > 5

-5 < x < 3

x < 3 or x > 5

x > 3 or x < -5

View answer & explanation

Correct answer is B

x2 + 2x > 15

x2 + 2x - 15 > 0

(x2 + 5x) - (3x - 15) > 0

x(x + 5) - 3(x + 5) >0

(x - 3)(x + 5) > 0

therefore, x = 3 or -5

i.e. x< 3 or x > -5

1,574.

Solve the inequality -6(x + 3) $\leq$ 4(x - 2)

x $\leq$ 2

x $\geq$ -1

x $\geq$ -2

x $\leq$ -1

View answer & explanation

Correct answer is B

-6(x + 3) $\leq$ 4(x - 2)

-6(x +3) $\leq$ 4(x - 2)

-6x -18 $\leq$ 4x - 8

-18 + 8 $\leq$ 4x +6x

-10 $\leq$ 10x

10x $\geq$ -10

x $\geq$ -1

1,575.

T varies inversely as the cube of R. When R = 3, T = $\frac{2}{81}$ , find T when R = 2

$\frac{1}{18}$

$\frac{1}{12}$

$\frac{1}{24}$

$\frac{1}{6}$

View answer & explanation

Correct answer is B

T $\alpha \frac{1}{R^3}$

T = $\frac{k}{R^3}$

k = TR³

= $\frac{2}{81}$ x 3³

= $\frac{2}{81}$ x 27

dividing 81 by 27

k = $\frac{2}{2}$

therefore, T = $\frac{2}{3}$ x $\frac{1}{R^3}$

When R = 2

T = $\frac{2}{3}$ x $\frac{1}{2^3}$ = $\frac{2}{3}$ x $\frac{1}{8}$

= $\frac{1}{12}$